Chapter 4, Problem 22SGR

To determine

To find: The coordinates of the image after rotation of $180$ degrees of the given image.

Answer to Problem 22SGR

The coordinates of the image of the triangle are $A^{\prime }\left(-5,-4\right)$ , $B^{\prime }\left(-3,2\right)$ and $C^{\prime }\left(1,-1\right)$ .

Explanation of Solution

Given:

The given image of the triangle is as:

  

In order to find the coordinates of the image of the triangle, first, multiply by $-1$ the $x$ coordinates and the $y$ coordinates of the given coordinates $A,B,C$ .

The image after transformation is given as:

  

The coordinates of the image of the triangle are calculated by using above graph is given as:

  $A^{\prime }\left(-5,-4\right)$ , $B^{\prime }\left(-3,2\right)$ and $C^{\prime }\left(1,-1\right)$ .

Therefore, the coordinates of the image of the triangle are $A^{\prime }\left(-5,-4\right)$ , $B^{\prime }\left(-3,2\right)$ and $C^{\prime }\left(1,-1\right)$ .